Probability and Statistical Inference

by Robert V. Hogg, Elliot Tanis

BOOK Written by two leading statisticians, this applied introduction to the mathematics of probability and statistics emphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation. Designed for students with a background in calculus, this book continues to reinforce basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts. NEW TO THIS Content updates TABLE OF Preface Prologue 1. Probability 1.1 Basic Concepts 1.2 Properties of Probability 1.3 Methods of Enumeration 1.4 Conditional Probability 1.5 Independent Events 1.6 Bayes's Theorem 2. Discrete Distributions 2.1 Random Variables of the Discrete Type 2.2 Mathematical Expectation 2.3 The Mean, Variance, and Standard Deviation 2.4 Bernoulli Trials and the Binomial Distribution 2.5 The Moment-Generating Function 2.6 The Poisson Distribution 3. Continuous Distributions 3.1 Continuous-Type Data 3.2 Exploratory Data Analysis 3.3 Random Variables of the Continuous Type 3.4 The Uniform and Exponential Distributions 3.5 The Gamma and Chi-Square Distributions 3.6 The Normal Distribution 3.7 Additional Models 4. Bivariate Distributions 4.1 Distributions of Two Random Variables 4.2 The Correlation Coefficient 4.3 Conditional Distributions 4.4 The Bivariate Normal Distribution 5. Distributions of Functions of Random Variables 5.1 Functions of One Random Variable 5.2 Transformations of Two Random Variables 5.3 Several Independent Random Variables 5.4 The Moment-Generating Function Technique 5.5 Random Functions Associated with Normal Distributions 5.6 The Central Limit Theorem 5.7 Approximations for Discrete Distributions 6. Estimation 6.1 Point Estimation 6.2 Confidence Intervals for Means 6.3 Confidence Intervals for Difference of Two Means 6.4 Confidence Intervals for Variances 6.5 Confidence Intervals for Proportions 6.6 Sample Size. 6.7 A Simple Regression Problem 6.8 More Regression 7. Tests of Statistical Hypotheses 7.1 Tests about Proportions 7.2 Tests about One Mean 7.3 Tests of the Equality of Two Means 7.4 Tests for Variances 7.5 One-Factor Analysis of Variance 7.6 Two-Factor Analysis of Variance 7.7 Tests Concerning Regression and Correlation 8. Nonparametric Methods 8.1 Chi-Square Goodness of Fit Tests 8.2 Contingency Tables 8.3 Order Statistics 8.4 Distribution-Free Confidence Intervals for Percentiles 8.5 The Wilcoxon Tests 8.6 Run Test and Test for Randomness 8.7 Kolmogorov-Smirnov Goodness of Fit Test 8.8 Resampling Methods 9. Bayesian Methods 9.1 Subjective Probability 9.2 Bayesian Estimation 9.3 More Bayesian Concepts 10. Some Theory 10.1 Sufficient Statistics 10.2 Power of a Statistical Test 10.3 Best Critical Regions 10.4 Likelihood Ratio Tests 10.5 Chebyshev's Inequality and Convergence in Probability 10.6 Limiting Moment-Generating Functions 10.7 Asymptotic Distributions of Maximum Likelihood Estimators 11. Quality Improvement Through Statistical Methods 11.1 Time Sequences 11.2 Statistical Quality Control 11.3 General Factorial and 2 k Factorial Designs 11.4 Understanding Variation A. Review of Selected Mathematical Techniques A.1 Algebra of Sets A.2 Mathematical Tools for the Hypergeometric Distribution A.3 Limits A.4 Infinite Series A.5 Integration A.6 Multivariate Calculus B. References C. Tables D. Answers to Odd-Numbered Exercises

Genres: Mathematics, Textbooks, Nonfiction, Reference, Science, Academic

648 pages, Hardcover

First published January 1, 1977

Reviews

[Anna]

I'm reading the 4th edition, from 1993.

[Steve Stuart · Rating 4 out of 5]

This is a very solid textbook on probability and statistics, from the introductory level through intermediate topics, and is reasonable as a reference text as well. The text tends to be dry, rather than chatty, and the topics are developed from scratch or described with proofs, rather than simply being presented as definitions. I consider these to be positive features, in a math text. The examples don't tend to be very interesting, but there are a large number of them, which helps when using this book as a student.

I used the second edition of this book in college. Despite having a large selection of newer, more comprehensive, or more advanced books on my shelf to choose from, Hogg & Tanis is still the book I normally turn to when I need to look up a distribution or statistical test.

[Jamiu Afolabi · Rating 5 out of 5]

A self explanatory book which with a detailed analysis on probability distributions, point estimation and interval estimation techniques. Prerequisite includes understanding of Calculus

[Goo]

This was sent to me by mistake when I ordered some other statistics book.

Looks worse than the regulars (C&B, Hogg & Craig, etc.).

[Adam · Rating 5 out of 5]

The prose is clear, the examples are valuable, the development is very quick to arrive at useful results. I find it walks a very satisfying balance between theory and application, giving proofs everywhere, and only where, the value of seeing the proof outweighs the time required to understand it. It and its associated Introduction to Mathematical Statistics are classics for a good reason.

However, as a classic, it is missing some more modern topics like survival functions.

[Bill]

I think this is a great introduction to statistics. There are a lot of well-thought of books which are complete nonsense. It was refreshing to find a book which is both accessible and rigorous.

I'm actually reading the 4th edition, not the 6th. It was really cheap on Alibris, and how much does statistics change, anyway?